Classical mechanics Assignment

Classical mechanics Assignment Words: 1309

The book has been written keeping in mind the general weakness in understanding the fundamental concept of the topic. The book is self-explanatory and adopts the “Teach Yourself” style. It is based on question-answer pattern. The language of book is quite easy and understandable based on scientific approach. Any further improvement in the contents of the book by making corrections, omission and inclusion is keen to be achieved based on suggestions from the reader for which the author shall be obliged.

I acknowledge special thanks to Mr.. Eraser Banyan, Chairman,Dry. Sandy Banyan, Director (Cad. ) Banyan Group of Colleges & Mr.. Mannish Banyan, Director Banyan International Institute of Engineering & Technology, who is the backbone and main concept provider and also have been constant source of motivation throughout this endeavourer. We also extend our thanks to M/s. Hastily, Amphora’s Augural/Sunnis Kumar Gain, Jasper, who played an active role in co-ordination the various stages of this endeavourer and spearheaded the publishing work.

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I look forward to receiving valuable suggestions from professors of various educational institutions, other faculty members and the students for improvement of the quality of the book. The reader may feel free to send in their comments and suggestions to the under mentioned address. Author Content Chapter. No. Name of Topic System of forces, Fundamental laws of mechanics, theorem, Rectilinear motion, plane curvilinear motion, Projectile motion, Newton’s law of motion, Telemeter’s principle. Moments and couple, Variation’s theorem, condition of equilibrium. Impulse, momentum, Impulse – Momentum relation, Impact. 3 Types of support and loading, reaction, Analysis of simple trusses by methods of Joints and method of sections. 4 Laws of Coulomb friction, Ladder, Wedges, Belt friction and rolling, Principle of virtual work and its applications. 5 Location of centered and center of gravity, area moment of inertia, mass moment of inertia. 6 Work, energy (Potential, Kinetic and Spring), Work – Energy relation, Law of conservation of energy,

Constrained motion of connected particles Syllabus Unit-I System of forces, Fundamental laws of mechanics, Composition of forces Free body diagram, Lama’s theorem Moments and couple, Variation’s theorem, condition of equilibrium Types of support and loading, reaction, Analysis of simple trusses by methods of Joints and method of sections Unit- II virtual work and its applications unit – Location of centered and center of gravity, area moment of inertia, mass moment of inertia Law of machines, Variation of mechanical advantages, efficiency, reversibility of machine Pulleys, wheel and axle, wheel and differential axle Transmission of power through belt and rope Kinematics of Particle .

Rectilinear motion, plane curvilinear motion, Projectile motion . Constrained motion of connected particles Dynamics of Particle and Rigid Body Newton’s law of motion Telemeter’s principle Unit-V Work and Energy . Work, energy (Potential, Kinetic and Spring) . Work – Energy relation . Law of conservation of energy Impulse and Momentum Impulse, momentum Impulse – Momentum relation, Impact Vibration . Un-damped Free vibrations Chapter – 1 Introduction this course on Engineering Mechanics, we shall be learning about canonical interaction between bodies. That is we will learn how different bodies apply forces on one another and how they then balance to keep each other in equilibrium.

That will be done in the first part of the course. So in the first part we will be dealing with STATIC. In the second part we then go to the motion of particles and see how does the motion of particles get affected when a force is applied on them. We will first deal with single particles and will then move on to describe the motion of rigid bodies. Q. L What is Force? NAS. :- Force is the action of one body on another. It may be defined as an action which changes the state of rest or of uniform motion of body. For representing the force acting on the body, the magnitude of the force, its point of action and direction of its action should be known.

According to Newton ‘s second law of motion, we can write force as F = ma = There are different type of forces such as gravitational, frictional, magnetic, inertia or those caused by mass and acceleration. Q. 2 What is Force system? NAS. :- A force system is the collection of forces acting on a body in one or more planes. According to the relative position of the line of action of the forces, the forces ay be classified as : Collinear, Coplanar, Concurrent, Coplanar concurrent, Non- coplanar concurrent, Coplanar non-concurrent, Non-coplanar non-concurrent. A force system has resultant forces, which is a single force which can be replaced a system of forces and produce the same effect on the body. Q. What is Parallelogram law of Forces? NAS. :- If two forces, acting at a point, are represented in magnitude and direction by the two sides of a parallelogram drawn from one of its angular points, their resultant is represented both in magnitude and direction by the diagonal of the parallelogram assign through that angular point. Resultant Force: If two or more forces P, Q, S, act upon a rigid body and if a single force, R, can be found whose effect upon the body is the same as that of the forces P, Q, S, this single force R is called the resultant of the other forces. Resultant of forces acting in the same direction (same straight line) is equal to their sum.

Third Law: Newton’s third law states that if a body A applies a force F on body B , then B also applies an equal and opposite force on A . (Forces do not cancel such other as they are acting on two different objects) Figure 1 Thus if they start from the position of rest A and B will tend to move in opposite directions. You may ask: if A and B are experiencing equal and opposite force, why do they not cancel each other? This is because – as stated above – the forces are acting on two different objects. Q. 3 A person walks mm to the east and mm to the north to reach his friend’s house. What is the total displacement of the person, and what is the total distance traveled by him? Sol. – Recall that distance is a scalar quantity. Thus the total distance covered is displacement, we add the two vectors to get a displacement of mm at an angle from east to north (Figure). Q. 14 Two persons are pushing a box so that the net force on the box is NON to the east If one of the person is applying a force AN to the north, what is the force applied by the other person. Sol. :- Let the force by person applying AN be denoted by errors by . We then have so that and that by the other Solution for angle of is given graphically in figure. The force comes out to be NON at an from east to south. Figure Chapter – 2 Q. 2 What do you understand by Equilibrium? NAS. – In the static part when we say that a body is in equilibrium, what we mean is that the body is not moving at all even though there may be forces acting on it. (In general equilibrium means that there is no acceleration I. E. , the body is moving with constant velocity but in this special case we take this constant to be zero). Let us start y observing what all can a force do to a body? One obvious thing it does is to accelerate a body. So if we take a point particle P and apply a force on it, it will accelerate. Thus if we want its acceleration to be zero, the sum of all forces applied on it must vanish. This is the condition for equilibrium of a point particle.

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